If you work out the balance with the bank they can not do this.
Respectfully, they do it all the time, if you owe a deficiency. With that being said, if you work out a payment plan for the deficiency, they may not but in most cases the debtor defaults on the agreement. Get it in writing!! Am sure that most lenders have their collateral contracts wrote differently. I would read your contract!
I deal with this everyday.
Like I said.